We report a new measurement of the n=2 Lamb shift in Muonium. Our result of 1047.2(2.3)_{stat}(1.1)_{syst} MHz comprises an order of magnitude improvement upon the previous best measurement. This value matches the theoretical calculation within 1 standard deviation allowing us to set limits on Lorentz and CPT violation in the muonic sector, as well as on new physics coupled to muons and electrons which could provide an explanation of the muon g-2 anomaly.